solve the system (x^3)(y^3)(z^4)=1 and (x^2)(y^4)(z^4)=2 and (x^2)(y^3)(z^5)=3

`(x^3)(y^3)(z^4)=
1................(1)`

`(x^2)(y^4)(z^4)=
2..................(2)`

`(x^2)(y^3)(z^5)= 3
....................(3)`

First, we will divide (1) by
(2).

==> `x/y = 1/2 ==> y= 2x
..................(4)`

``Now we will divide (1) by
(3).

`==> x/z = 1/3 ==> z =
3x...................(5)`

Now, we will substitute (5) and
(5) into (1).

`==> (x^3)(y^3)(z^4) =
1`

`==> (x^3)(2x)^3 (3x)^4 =
1`

`==> (x^3)(8x^3)(81x^4)=
1`

`==> 648x^10 =
1`

`==> x^10 =
1/648`

`==> x =
(1/648)^(1/10)`

`==> y= 2x =
2/(648)^(1/10)`

`==> z= 3x = 3/
648^(1/10)`

``